**View:**

**Sorted by:**

### How to Find a Wave-Function Equation in an Infinite Square Well

Infinite square well, in which the walls go to infinity, is a favorite problem in quantum physics. To solve for the wave function of a particle trapped in an infinite square well, you can simply solve [more…]

### How to Find the Wave Function of the Ground State of a Quantum Oscillator

In quantum physics, you can find the wave function of the ground state of a quantum oscillator, such as the one shown in the figure, which takes the shape of a gaussian curve. [more…]

### How to Use Creation and Annihilation Operators to Solve Harmonic Oscillator Problems

Creation and annihilation may sound like big make-or-break-the-universe kinds of ideas, but they play a starring role in the quantum world when you're working with harmonic oscillators. You use the creation [more…]

### How to Shift the Symmetric Square Well Around the Origin

Infinite square wells, in which the walls go to infinity, are a favorite in quantum physics problems. In some instances, you may want to shift things so that the square well is symmetric around the origin [more…]

### How Particles Pass Through Potential Barriers That Have Less Energy

When you are working with potential barrier of height V_{0} and width *a* where E > V_{0}, this means that the particle has enough energy to pass through the potential barrier and end up in the [more…]

### How to Find the Energy Eigenstate of a Harmonic Oscillator in Position Space

In quantum physics, you can use operators to determine the energy eigenstate of a harmonic oscillator in position space. The charm of using the operators [more…]

### How to Find Any Excited State of a Harmonic Oscillator

If you can determine the wave function for the ground state of a quantum mechanical harmonic oscillator, then you can find any excited state of that harmonic oscillator. [more…]

### How to Find the Energy Level of a Harmonic Oscillator: An Example

Your quantum physics instructor may ask you to find the energy level of a harmonic oscillator. The best way to learn how is through an example. Say that you have a proton undergoing harmonic oscillation [more…]

### How to Solve the Schrödinger Equation for Free Particles

There are plenty of free particles — particles outside any square well —in the universe, and quantum physics has something to say about them. The discussion starts with the Schrödinger equation: [more…]

### How to Estimate a Particle's Location by Applying Schrödinger's Equation to a Wave Packet

If you have a number of solutions to the Schrödinger equation, any linear combination of those solutions is also a solution. So that’s the key to getting a physical particle: You add various wave functions [more…]

### How Particles Tunnel Through Potential Barriers That Have Greater Energy

When a particle doesn't have as much energy as the potential of a barrier, you can use the Schrödinger equation to find the probability that the particle will tunnel through the barrier's potential. You [more…]

### Measuring the Energy of Bound and Unbound Particles

In quantum physics, you can solve for the allowable energy states of a particle, whether it is bound, or trapped, in a potential well or is unbound, having the energy to escape. [more…]

### How to Find Square-Well Energy Levels

In quantum physics, if you know the boundary conditions of a square well, you can find theenergy levels of an electron.

The equation [more…]

### How to Find the Normalized Wave Function for a Particle in an Infinite Square Well

In quantum physics, if you are given the wave equation for a particle in an infinite square well, you may be asked to normalize the wave function. For example, start with the following wave equation: [more…]

### Find the Wave Function of a Particle in an Infinite Square Well over Time

In quantum physics, you can use the Schrödinger equation to see how the wave function for a particle in an infinite square well evolves with time*.* The Schrödinger equation looks like this: [more…]

### How to Find the Eigenfunctions of L^{2} in Spherical Coordinates

Your quantum physics instructor may ask you to find the eigenfunctions of L^{2} in spherical coordinates. To do this, you start with the eigenfunction of [more…]

### How to Determine Harmonic Oscillator Eigenstates of a System

In quantum physics, when you have the eigenstates of a system, you can determine the allowable states of the system and the relative probability that the system will be in any of those states. [more…]